{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Решение задачи Коши для одного ОДУ\n",
    "Задача Коши – это задача для обыкновенного дифференциального уравнения (ОДУ), в которой известны начальные условия. Для решения задачи Коши вы можете использовать библиотеку scipy в Python. Вот пример решения задачи Коши для простого ОДУ\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Определяем дифференциальное уравнение\n",
    "def ode(x, y):\n",
    "    dydx = -2 * y\n",
    "    return dydx\n",
    "\n",
    "# Начальные условия\n",
    "x0 = 0.0  # Начальная точка\n",
    "y0 = 1.0  # Начальное значение y(0)\n",
    "\n",
    "# Интервал интегрирования ОДУ\n",
    "x_span = (0.0, 5.0)  # От 0 до 5\n",
    "\n",
    "# Решение задачи Коши\n",
    "sol = solve_ivp(ode, x_span, [y0], t_eval=np.linspace(x_span[0], x_span[1], 100))\n",
    "\n",
    "# Извлечение результатов\n",
    "x_values = sol.t\n",
    "y_values = sol.y[0]\n",
    "\n",
    "# Построение графика решения\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_values, y_values, label='Решение', color='blue')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y(x)')\n",
    "plt.title('Решение задачи Коши для ОДУ')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Решение линейного уравнения 2-ого порядка\n",
    "#с начальными условиями y(0)=0 и y′(0)=1. Мы решим это уравнение и построим график решения.\n",
    "\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Определяем дифференциальное уравнение второго порядка\n",
    "def ode(x, y):\n",
    "    dydx = np.zeros_like(y)\n",
    "    dydx[0] = y[1]\n",
    "    dydx[1] = -2 * y[1] - y[0]\n",
    "    return dydx\n",
    "\n",
    "# Начальные условия\n",
    "x0 = 0.0  # Начальная точка\n",
    "y0 = [0.0, 1.0]  # Начальные значения y(0) и y'(0)\n",
    "\n",
    "# Интервал интеграции\n",
    "x_span = (0.0, 15.0)  # От 0 до 5\n",
    "\n",
    "# Решение дифференциального уравнения\n",
    "sol = solve_ivp(ode, x_span, y0, t_eval=np.linspace(x_span[0], x_span[1], 100))\n",
    "\n",
    "# Извлечение результатов\n",
    "x_values = sol.t\n",
    "y_values = sol.y[0]\n",
    "\n",
    "# Построение графика решения\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_values, y_values, label='Решение', color='blue')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y(x)')\n",
    "plt.title('Решение линейного дифференциального уравнения 2-го порядка')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.integrate import solve_ivp, odeint\n",
    "\n",
    "g = 9.81\n",
    "l = 0.1\n",
    "\n",
    "\n",
    "def f(t, r):\n",
    "    omega = r[0]\n",
    "    theta = r[1]\n",
    "    return np.array([-g / l * np.sin(theta), omega])\n",
    "\n",
    "\n",
    "time = np.linspace(0, 10, 1000)\n",
    "init_r = [0, np.radians(179)]\n",
    "\n",
    "results = solve_ivp(f, (0, 10), init_r, method='RK45', t_eval=time, rtol=1e-8)\n",
    "cenas = odeint(f, init_r, time, tfirst=True)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "\n",
    "ax1.plot(results.t, results.y[1])\n",
    "ax1.plot(time, cenas[:, 1])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "https://stackoverflow.com/questions/56153628/using-scipys-solve-ivp-to-solve-non-linear-pendulum-motion\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.integrate import solve_ivp, odeint\n",
    "\n",
    "g = 9.81\n",
    "l = 0.1\n",
    "\n",
    "\n",
    "def f(t, r):\n",
    "    omega = r[0]\n",
    "    theta = r[1]\n",
    "    return np.array([-g / l * np.sin(theta), omega])\n",
    "\n",
    "\n",
    "time = np.linspace(0, 10, 1000)\n",
    "init_r = [0, np.radians(179)]\n",
    "\n",
    "results = solve_ivp(f, (0, 10), init_r, method=\"RK45\", t_eval=time) #??????\n",
    "cenas = odeint(f, init_r, time, tfirst=True)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "\n",
    "ax1.plot(results.t, results.y[1])\n",
    "ax1.plot(time, cenas[:, 1])\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
